Problem: Suppose that $\alpha$ is inversely proportional to $\beta$.  If $\alpha = -3$ when $\beta = -6$, find $\alpha$ when $\beta = 8$.  Express your answer as a fraction.
Since $\alpha$ is inversely proportional to $\beta$, by definition $\alpha\beta = k$ for some constant $k$.  Plugging in, we see that $(-3)\cdot (-6) = k$, so $k = 18$.  So when $\beta = 8$, we have that $8\alpha = 18$, or $\alpha = \boxed{\frac{9}{4}}$.